I have similar concerns about the watering amount.
I have a mother plant with many younger plants in a 30 gallon container and am wondering what I should do with it over the winter.
Should I put them in the garage or push them up against the house for ambient warmth and to keep the snow off or just leave them where they are?

This is my first time growing strawberries in a container so I'm not really sure what kinds of issues I will be dealing with here.

As someone who grows strawberries in containers in the Seattle area (without covering them or anything) I can rather safely say that these little beasties will do well in damp conditions. I'm not sure how much freezing or snow they'll handle but with all of the rain we get in a winter (constant light rain) I've never had any issues.

Since you did not say we are assuming you have them planted in well drained mix as recommended on this forum. If that is the case they should be fine in their containers outdoors through the winter in most zones. Al

I grow strawberries in double 5-gal SWC's in Zone 4b and overwinter them with good success.

Once you get consistently freezing nights, remove all blossoms and runners that have not been rooted. Also remove all dead leaves. Water well, or until water runs into the reservoir. Allow to drain overnight. Empty water from the reservoir and fill reservoir with dried leaves or straw. Pack well as this will serve as insulation for the roots. Replace inner bucket. Move buckets against a north facing wall of a garage or home. Make a row of straw bales to protect the buckets. Cover the buckets with floating row cover to keep straw and leaves out of the buckets, then pile on dried leaves and a thick layer of straw.